Gear tooth



- Jan. 11, 1927. 1

1,613,702 S.- A. S. HAMMAR v 5 GEAR TOOTH Original Filed May 20. 1920 at 1 INVENTOR S'yarZfl-W v ATTORNEYS I ,613 702- Jan. 11,1927 s. A a HAMMAR 1 can moon; Original F/il ed May 20, 1920 2 sham-sheet 2 mvmrok A TTORNEYS atented Jan. 11, 1927.

SIGABD A. S. HAMMAR, 0F BETHLEHEM, PEI .VNSJZL'VANIA.

' GEAR. roo'rn.

Continuation of application Serial No. 382,907, filed May 20, 1920. This application filed June 15, 1922."

- Serial No. 568,502.

This invention relates to gear teeth and has reference more particularly to gear teeth stepped to increase their strength and to accomplish improvements which will be explained in this, specification and is a con-' tinuation of my application Serial No. 382,907, filedoMay 20, 1920, entitled Gear teeth. I

In the construction of gears to accomplish tain gear wheels of a certain size and weight which give the desired strength. The weal;- est point of gear teeth of the usual construction is at the base and .in order to provide gear teeth having a maximum strength attention must be directed to the strengthening of the gear teeth at the base. It was to solve this problem that the invention to be describedin the following specification was devised.

The formula fOI iZlIG strength of a cantilever beam is as follows:

61 1 where is thewidth of the beam, t is the thickness of the beam at the support, Z is the length of the beam extending beyond the support, S is the maximum allowable stress, P is the load which, if applied to the end of the beam, will produce the stress S.

This formula may be applied to the strength of gear teeth, and it. is evident from inspection of the formula that gear teeth may be strengthened (l) by increasing the face of the tooth or (f); (2) by reducing the length of the tooth and (3) by increasing the thickness of the tooth (t). The face of the tooth may be increased within certain limits, but the weight of the gear is likewise increased in the same proportion as the strength. The length of the ,tooth can also be decreased only to a certain limit. The thickness (t) at the root is governed by the thickness at the pitch circle, which is limited to bne-half the pitch in thecase of teeth of the present standard construction. To increase the thickness is therefore equivalent to increasing the pitch, and assuming that the teeth of this new pitch are of the same shape as the teeth of the old pitch, and the 'new gear of the same shape asthe old gear, it is easily shown .that the increase in strength, as measured by the maximum allowable bending moment, isaccompanied by increase in weight in more than directproportion.

The aforementioned formula can be written as follows:

Sft

which assuming that S, f, and P are constant, may be written z:Kr 3

Equation 3 resembles the typical formula for a parabola;

2 pwzg 4 aflzKy 5 Thus it is seen that in order to make a gear tooth of uniform strength throughout its length, the tooth must/have a parabolic outline. However, a tooth with a parabolic outline would not have the requisite characteristics of a gear tooth which is to give a constant speed with the minimum of friction.

tooth and metal added at its base so that.

the thickness at the base is increased and the thickness of the tooth at the successive steps is the same asthe thickness at corresponding points of a beam of parabolic outline, or

approaches this condition more nearly than does an unstepped tooth.

As will be shown hereafter a stepped tooth is not only thicker at the root for a given' pitch but it is also shorter for a given angle of contact, and as the strength of a tooth'is proportional to the square of its thickness and inversely proportional to its length it can be. seen that the increase in strength to be realized by stepping a tooth is very great.

*An advantage which I claim for the stepped a given tactof length of tooth. The angle of cona tooth is that angle through which tooth is greater angle of contact for subtended by the involute curvature ofthe 'tooth. For a stepped tooth the angle of contact equals the sum of the angles of contact of the composing sections, or, in other words, the angle of contact of the stepped tooth equals the angle of contact-of the unstepped tooth plus the sum of the angles subtended by the steps or shoulders on one side. of the tooth. The greater angle of contact is particularly valuable when the number of teeth is very small. If an increased angle of contact is not required, the teeth may be made shorter, thus adding to the strengthof the tooth and reducing friction, which is greater for long teeth than for short teeth, as portions of a tooth lying farther from the pitch circle slip more than parts lying nearer the same.

'is that gears, having teeth of this description 7 for a given horsepower to be transmitted,

may be considerably smaller than gears having unstepped teeth. .This means not only saving in first cost and in the space occupied, but also, owing to reduced circumferential velocity, less noise in operation and reduced stresses in the metal of the teeth.

Since a gear with stepped teeth, in transmitting a given horsepower, will be smaller and run at a lower peripheral velocity than a gear with unstepped'teeth, and there is a limit to the peripheral speed at which a gear may be-run, itfollows that the maximum power which can be transmitted byv stepped teeth is greater than the which can be transmitted by unstepped teeth.

When used on infernal gears the superiority of stepped teeth is very striking. As

each section of astepped-tooth is shorter than a whole tooth, it follows that the sec' tions will clear after disengagement more readily than will the-whole tooth when, it is unst-epped. Therefore the pinion may, for a given pitch and length of tooth, be made much larger in proportion tothe gear and,

by introducing a suiiicient number of steps,

. the gear and pinion may diifer by as little as one tooth, and yet the pitch, length of tooth, number of, teeth,\angle of contact, etcL, be anything desired. It is evident that by this means the greatest powers may be transmitted and, when used in differential action, one .pair of gears, and these smaller than the first pair of gears in a train of gears of theiusual form, be made to do the service of the whole gear train, resulting in simpler construction and the 'almost complete elimination of friction, wear and noise. Where the teeth are oblique as are worm threads, spiral teeth, etc.', more than one section of the stepped tooth are in contact at the same time, This maximum power the .the wear of the teeth.

I am aware that variable motionhas been obtained by usinggears having various .series of teeth, each series with its own'tooth characteristics such as pitch circle, addendum and dededum as shown in Patent No. 466,923 to Price. However, in the Price pat-- ent the object is to obtain a variable motion between the shafts which is obtained by making each tooth in each itself.

Reference is to .be had to the accompanying drawing forming a part of this specificationin which it is understood that the drawing illustrates only one form of the'invention with certain modifications, and in which Figure 1 is a fragmentary elevation of my improved gear teeth; v

Figure 2 is a fragmentary elevation of a a modified form of my improved gear teeth; Athird point in favor of the stepped tooth Figure 3 is a fragmentary elevation-of a second modified form of my gear teeth;

series complete in Figure 6.is a drawing of one of the teeth of the same pinion at the point of rotation where the first and second section of a tooth are in contact at the same time;

' Figure 7 is a View showing the second and third sections of a'tooth in contact at the same time;

Figure 8 is an enlarged view showing the second and'thirdsections of a tooth in con-- tact at the same time;

Figure 9 is a view showing a stepped tooth in full lines and an unstepped tooth in dot ted lines, both having the same angle of contact and also showing the line of action.

Referring to the above-mentioned drawings, a pinion 10 and a gear 11 are shown. Gear teeth of ordinary construction will have the shape shown by the dotted lines 14 inFigures '1, 3 and 4, and with this shape weakest part of the tooth is at the base.

'lheoretically as pointed out'previouslyin the specification, a tooth having auniiorm strength throughout its length would be parabolic in outline *as shown by the dotted lines 15 in Figures- 1 and 3. In orderto strengthen the base of the tootli, I remove metal from the end of the tooth wherethe tooth is strongest, and add metal at the base of the tooth so asto form one or'more steps or shoulders 16. In this manner and by correctly dimensioning the steps, I form a tooth of two or more stepped portions or sections 17, the thickness at the base of each portion being approximately a double m-dinate of a parabola whose vertex lies in that point on the center line of the tooth in which the load may be considered applied when the end of the tooth is engaged. [n the modification shown. in Figure 4, one side of the tooth has the unstepped outline of a standard gear tooth while the opposite side is stepped. The steps are twice as great as when both sides are stepped and the strength is the same.

This is an important construction of gears, which run always in the same direction, as in this matter, making the stepped side the working side the increase in the angle of contact is twice as great as when both sides are stepped. If the unstepped side is the working side it is not necessary to provide for continuous contact.

Referring to Figures 5, 6 and 7, an internal gear 11 and a pinion are shown with stepped teeth formed thereon. The shoulders 16 and the sections 1'7 are formed in the same manner as described in the precedingparagraphs.

It is a well known fact that in order to cause gear teeth to transmit a perfectly uniform motion, the normal to the tooth surfaces at the point of contact must always pass through the point of tangency of the pitch circles of the gear and' pinion. In order to accomplish this, I so shape the contact surfaces on the successive stepped portions or sections 17, that the aforementioned conditions are fulfilled and a perfectly uni-'' form motion will be transmitted by'thegear 'teeth. In otherwords, each of the stepped portions on'the tooth are constructed with reference to a common pitch circle so as to obtain a uniform speed with a minimum of friction, while in the patent to Price. each series of teeth is constructed with reference to its own individual pitch circle so that a variable speed is obtained. It is clear that as long as the sections of a tooth have a common pitch circle, it-is not necessary that the corner or sinus of the same.

Tn the form shown in Figure 3, two shoulders 16 are formed on the teeth so as to form three stepped portions on each side of the tooth. .the contact surfaces being shaped sub stantially according to the aforementioned rule. It isunderstood that my teeth may be made involute, cycloidal. or by any other desired system, and different sections of the is being passed.

same teeth may conform to different systems.

The gears shown in, Figure 5 have. teeth of three sections intercepted by two steps. Beginning at the root of the pinion tooth, the first section is a 20 degree involute, the second section a degree involute. Figure (3 shows a point in the rotation of the gears, where both these sections are in contact. As the step is inside the pitch circle, the degree line of action lies inside the 15 degree line of action. 'lhereforeif the first section is a 20 degree involute and the second section a 15 degree involute,-there is an angleof 5 degrees bet-ween the'lines of action of the two sections and a corresponding clearance space between the shoulder of the pinion and the shoulder of the gear. This space may be utilized so, that the second section engages before the first section disengages without undercutting either shoulder of the engaging teeth with reference to its line of action. If the arrangement were reversed and the first section were a 15 degree involute and the second section a 20 degree circle. Therefore the 20 degree line of acthe rotation of the gears where sections 2 and 3 are in contact at the same time are shown on an enlarged scale in Figure 7.

It willbe nni'erstood'that teeth thus constructed willhave acommon ,pitch circle and two base circles.

In the greatma ority of cases it is not necessary to make provision for continuity of contact from one section to the next of the sail-2e tooth, or to make the shoulder of any specific outline. All spiral and helical gears are exempt from this necessity, as are also all spur and bevel gears, wh'ose'angle of contact exceeds the. pitch angle, that is, the angle'sul'ltended. by one tooth and space, sufiiciently to allow the preceding or succeeding tooth to biz engaged while the step For instance, if we have a lti-tooth 20 degree involute stepped pinion and the engagement with the gear com mences in the point where the line of action is tangent to the base circle, the angle of contact being 38 degreesythen, if the first step crosses the line of action within 15 degrees of the said tangent point. the preceiling tooth will be still engaged, and if the second step passes the line of action after the tooth has'been in contact 22 degrees, the following tooth will have entered into engagement. Such a location of the steps would be very satisfactory, but, if for the same angle of contact, we had a pinion of 10 teeth, it is evident that the steps would have to be located too near to myself strictly to the mechanical details herein illustrated, since manifestly the same can be considerably varied without departure from the spirit of the invention as defined in the appended claims. While it is de- 'sira'ble that the steps should beiso arranged that the teeth of two meshing gearsare equally strong and the strength of the teeth the maximum which can be realized with a given number of steps, it is often preferable to modify theteet-h. So, for instance,

' the steps may be made lar'ger in order to realize a greaterang'le of contact or smaller for the purpose of modifying the contour of the shoulder or they may be made either smaller or larger for the sake of meshing with the teeth of other gears or for the purposes of interchangeabilityand standardization.

Thus, if the gears are standardized and the smallest ge'ar'of a certain standard sethas teeth whose sections'follow the geometric -rogressiono'f the true parabola none of the larger gears of the same set. can follow the same progression exactly. Furthermore, there are other advantages to be derived from the invention besides increase in strength and in endeavoring to realize these to the fullestextent it may be necessary to modify the thickness of the tooth sections. As regards strength the object of the invention is fulfilled when every section 'of the teeth of two engaging gears will marry a .greater load than the weaker tooth of two engaging gears,-which are unstepped.

Claims: i

1. Gears haying teeth consisting of a series of steps constructed. so that the base of the tooth is made thicker due'to the steps than an unstepped toothof the same pitch and proportion, said steps being, adapted 'to increase the strength-0f the tooth, the contact faces of the successive sections being constructed substantially with reference to a common pitchcircle so that said gears run at a uniform speed with a minimum of friction. x

2. Gear teeth constructed with a series of steps and sections, the thickness of each sec- -tion' being such that the various sections are equally strained when the load is applied at, or near the point of the tooth, the contact surfaces of each tooth being constructed sub stantially withreference to a common pitch circle.

3. Gear teethconstructed with steps, the contact faces of each section being formed substantially with reference to a common pitch circle so that said gears run with a uniform speed and aminimum'of friction, the steps being so proportioned that all sections are strained equally when a load is applied at the end of. the tooth, and the bending moment istmaximum.

4. Gear teeth in steps, the curvature of each stepped portion being substantially the same as the curvature of that part of a correspondine unstepped tooth which is in the same rela 1V6 position with reference to the pitch circle.

5. Stepped gear teeth, the working faces of the successive step sections having substantially the same curvature as the corresponding successive elements of an unstepped tooth.

6. A gear having steppedteeth, the successive stepped sections being formed by curved lines, the curvature of each portion being governed by its position relatively to one common pitch-circle.

7 A gear having stepped teeth with the points of maximum stress at the, base of the successive steps on or near aparabola whose vertex lies approximately at the most extreme point where the maximum loadmay be applied. 7

8. Gears having stepped teeth, each step section joining the shoulder in a fillet which is sunk below the shoulder.

9. In gears, stepped gear teeth, the curvature of the successive stepped sections on,

both sides being the same as the curvature of the corresponding portions of an un stepped tooth.- 1

10. In gears, stepped gear teeth, the working surface of the teeth consisting of successive sections whose contours are lines-designed to make the gearrotate with uniform velocity.

11. In gears, stepped gear teeth, each face made up of two or more sections, the working surfaces of said sections consisting of lines of such nature that the contact passes from one section to the next without inter ruption.

12. In gears, stepped gear teeth, each working face of said gear teeth consisting of two or more sections, at least two. of which sections'make continuous contact.

13. Gear teeth having stepped faces, each working face of said' gear teeth consisting of two or more sections, one or more of the shoulders between said sections bein underw cut with reference to the center of t 1e gear.

14. Stepped gear teeth, each working face consisting of a plurality of sections,

the sections beingso arranged that when ya shoulder between two sections 1s lntersccted liy the line of action, the section of a 10 tooth other than that to which the shoulder belongs is in contact.

15. Gears, having stepped teeth, the sections being constiucted with reference to a common pitch circle but having more than 15 one base circle.

SIGARD A. s. HAMMAR. 

